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# FP1: Complex Numbers watch

1. The complex number z is given by

Find the modulus and argument of

Do I make into ?

Different question:
Then, the complex number z had modulus 2 and argument
Write z in the form
2. (Original post by Fool In The Rain)
The complex number z is given by

Find the modulus and argument of

Do I make into ?

Different question:
Then, the complex number z had modulus 2 and argument
Write z in the form
I have no idea what you are trying to do with the fraction thing...
EDIT: just read the actual question... err, yes the fraction thing is a good idea. However, it is hard to draw it on an argand diagram, or do much else with it either, if it is written in this form. Try to turn it into the form a + bj in a similar way to how you rationalised the denominator at GCSE.
For the modulus, think about plotting the complex number on an argand diagram. The modulus is the length of the line, so how would you work this out given the real and imaginary parts (hint: pythagoras...)
The argument is the angle between this line and the positive real axis (use trig).

To change from modulus argument form into component form, draw a diagram as before. Use trig to work out the real and imaginary components.
3. (Original post by Fool In The Rain)
The complex number z is given by

Find the modulus and argument of

Do I make into ?

Different question:
Then, the complex number z had modulus 2 and argument
Write z in the form
I'd do the first one by putting z into modulus/argument form, because it's really easy to take the reciprocal of something in the form .
The second one: dragonkeeper999 pretty much said what I wanted to say; a diagram is really useful.

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Updated: April 10, 2013
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